What is the probability of getting exactly 40 heads if a fair coin is tossed 50 times, using:

a) The binomial distribution formula?

b) The normal approximation to the binomial distribution?

MY ANSWERS:

a) p(x) = c(n,x) p^x q ^n-x

p(x=40) = c(50,40) (4/5)^40 (4/5)^10

Now would that be correct??? I do that and I get a ridiculous number.

b) SD(standard deviation)= Squareroot(SR) of =npq

Sd=SR 50x0.8x0.2

SD= SR = 8

SD= 2.83

z = 39.5 - 50/2.83 = -10.5/2.83 = -3.71

Using the z-score table 0.4999 = 49.9% of getting exactly 40 heads.

Something seems off, can someone direct me to where I am going wrong?